Question

Show all the vectors of (u+v)*(u-v)=||u||^2-||v||^2

Answer 1

Answer:

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Answer 2

Answer:

It is simple. Remember that a vector square equals its modulus square i.e. u^2 = u^2 for any vector u . Here

LHS = |u + v|^2 + |u -v|^2

= (u + v)•(u + v) + (u -v)•(u -v)

= (u^2 + v^2 + 2u•v) + (u^2 + v^2 -2u•v)

= 2[u^2 + v^2] = 2(u^2 + v^2) = RHS .